no. 2
On reduction of moduli schemes of abelian varieties with definite quaternion multiplications
[Sur la réduction des schémas de modules de variétés abéliennes à multiplication quaternionique définie]
Yu, Chia-Fu1
1 Institute of Mathematics, Academia Sinica and NCTS 6th Floor, Astronomy Mathematics Building No. 1, Roosevelt Rd. Sec. 4 Taipei, Taiwan, 10617
Annales de l'Institut Fourier, Tome 71 (2021) no. 2, pp. 539-613.

Dans cet article, nous faisons une étude initiale sur les espaces de modules de type D en caractéristique positive p≠2, où le nombre premier p peut être ramifié dans la donnée définissant l’espace de modules. Nous classifions explicitement les classes d’isogénie des groupes p-divisibles avec structures supplémentaires en question. Nous étudions également la réduction des espaces de modules de type D de rang minimal.

In this paper we make an initial study on type D moduli spaces in positive characteristic p≠2, where we allow the prime p to ramify in the defining datum. We classify explicitly the isogeny classes of p-divisible groups with additional structures in question. We also study the reduction of the type D moduli spaces of minimal rank.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/aif.3349
Classification : 14G35, 11G18
Keywords: Shimura varieties of type D, bad reduction, isocrystals
Mot clés : variétés de Shimura de type D, mauvaise réduction, isocristaux
Yu, Chia-Fu 1

1 Institute of Mathematics, Academia Sinica and NCTS 6th Floor, Astronomy Mathematics Building No. 1, Roosevelt Rd. Sec. 4 Taipei, Taiwan, 10617
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Yu, Chia-Fu. On reduction of moduli schemes of abelian varieties with definite quaternion multiplications. Annales de l'Institut Fourier, Tome 71 (2021) no. 2, pp. 539-613. doi : 10.5802/aif.3349. https://aif.centre-mersenne.org/articles/10.5802/aif.3349/

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